1. Statement of the Technical Field
The present invention relates to optical waveguides, and more particularly to Photonic Crystal Waveguides (“PCWs”) and optical isolators.
2. Description of the Related Art
PCWs can modify light propagation and dispersion characteristics through their periodic structures, thus have important applications in communications and sensing. Particularly, the slow light effect in a PCW can significantly enhance light-matter interaction, as demonstrated in significant reduction of interaction lengths for PCW based modulators and switches. To date, most of the PCW research has been focused on the TE-like mode with even symmetry. However, a PCW often has an odd TE-like mode inside the photonic bandgap exhibiting the slow light effect as well. This odd mode can potentially open up the opportunities for mode-symmetry-based novel devices, such as one-way waveguides that exploit indirect interband photonic transitions between even and odd modes. The slow light effect in PCWs can help reduce the interaction length for such transitions, enabling ultra-compact devices. To utilize this odd mode in any devices, it is crucial to control its excitation symmetry and understand its slow light spectral characteristics. Normally, this odd mode does not exhibit itself evidently in the PCW transmission spectrum because its odd symmetry prohibits its excitation by the fundamental even mode of a conventional waveguide typically used at input. Symmetry-breaking structure imperfections sometimes may induce some coupling to this odd mode, causing a decrease of PCW transmission in the odd mode band. But such imperfection-induced coupling between this odd mode and other modes is not controllable, and therefore is not useful in practice.